# Meaning of Pi 1 The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

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Meaning of Pi 1 The Meaning & Use of Pi by Joseph A. Castellano, Ph.D.

Meaning of Pi 2 How Pi (π) is Derived Take a circle of string, 1 meter in diameter, cut it, stretch it out and measure its length: d = 1 m L = 3.14159 m π = 3.14159 The length of the string is 3.14159 m. The circumference of every circle is always 3.14159 times its diameter. This constant is known as pi and denoted by the Greek letter, π.

Meaning of Pi 3 How Pi (π) is Used To calculate C, the circumference of a circle using the diameter, d or the radius, r: C. rr d d = 2 r C = π 2 r C = π d or

Meaning of Pi 4 How Pi (π) is Used To calculate A, the area of a circle using the radius, r:. r A = π r 2

Meaning of Pi 5 How Pi (π) is Used To calculate A, the area of a circle using the diameter, d:. d A = π d 2 ___ ___ 4

Meaning of Pi 6 How Pi (π) is Used To calculate the surface area of a sphere As, using the radius, r: As = 4 π r 2. r

Meaning of Pi 7 How Pi (π) is Used To calculate the volume of a sphere Vs, using the radius, r, or the diameter, d: Vs = 4/3 π r 3 or Vs = 1/6 π d 3. r

Meaning of Pi 8 Summary The circumference of a circle is 3.14159 times its diameter. This value is defined by the Greek letter π (Pi) The circumference of a circle, C is equal to: C = d π or C = 2 r π

Meaning of Pi 9 Summary The area of a circle, A, is equal to: The surface area of a sphere, As, is equal to: The volume inside a sphere, Vs, is equal to: As = 4 π r 2 Vs = 4/3 π r 3 or Vs = 1/6 π d 3 or A = (π d 2 )/4 A = π r 2

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